In this article we report on the first accurate quantum mechanical temperature-dependent rate constants for the two possible products of the (F+HD) system and on the corresponding intramolecular kinetic isotope effects. The calculations were done for the Stark-Werner and the Hartke-Stark-Werner potential energy surfaces. It was found that the two surfaces yield significantly different rate constants for both products but similar molecular kinetic isotope effects. These isotope effects are about two times larger than the experimental ones, at the lowest measured temperature region (160-200 K) but become rather close to them at similar to 400 K. The F+HD is known to exhibit, at the low energy region, various kinds of isotope effects. In the present study we revealed a new isotope effect related to the dependence of (integral) cross sections on the initial rotational states j(i) at intermediate energies. Whereas the cross sections to form DF are only mildly dependent on j(i) (at most 20% for j(0)=4) a very large effect-which at some energies (similar to 0.1 eV) enlarges the integral cross sections almost three times-is obtained for HF.